I feel your conflict of emotions, Meloncollie. Is there some form of 'birth control for mice' pellets you can strew in your garden? (Heard of such a thing for cockroaches.)
Is there a transportation tube from your garden to Ms Sutter's house (her rats might enjoy the company)?

P.S.
"I tried one of those ultra-sonic underground beeping thingies a few years ago, but the neighbors complained about the noise."
Are your neighbours mice or men?